A wide neighbourhood interior-point method with iteration-complexity bound for semidefinite programming

Optimization ◽  
2010 ◽  
Vol 59 (8) ◽  
pp. 1235-1246 ◽  
Author(s):  
Zengzhe Feng ◽  
Liang Fang
Keyword(s):  
Semidefinite Programming ◽  
Interior Point ◽  
Interior Point Method ◽  
Point Method ◽  
Iteration Complexity ◽  
Complexity Bound ◽  
Wide Neighbourhood

Simplified analysis of a full Nesterov–Todd step infeasible interior-point method for symmetric optimization

2015 ◽  
Vol 08 (04) ◽  
pp. 1550071 ◽  
Author(s):  
Behrouz Kheirfam
Keyword(s):  
Interior Point ◽  
Interior Point Method ◽  
Interior Point Methods ◽  
Point Method ◽  
Central Path ◽  
Complexity Bound ◽  
Symmetric Optimization ◽  
Iteration Bound ◽  
Infeasible Interior Point Method ◽  
Simplified Analysis

We give a simplified analysis and an improved iteration bound of a full Nesterov–Todd (NT) step infeasible interior-point method for solving symmetric optimization. This method shares the features as, it (i) requires strictly feasible iterates on the central path of a perturbed problem, (ii) uses the feasibility steps to find strictly feasible iterates for the next perturbed problem, (iii) uses the centering steps to obtain a strictly feasible iterate close enough to the central path of the new perturbed problem, and (iv) reduces the size of the residual vectors with the same speed as the duality gap. Furthermore, the complexity bound coincides with the currently best-known iteration bound for full NT step infeasible interior-point methods.

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